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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The radicals of a semigroup


Author: Rebecca Slover
Journal: Trans. Amer. Math. Soc. 204 (1975), 179-195
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-1975-0369584-6
MathSciNet review: 0369584
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Abstract: This paper investigates various radicals and radical congruences of a semigroup. A strongly prime ideal is defined. It is shown that the nil radical of a semigroup is the intersection of all strongly prime ideals of the semigroup. Furthermore, a semigroup with zero element is nil if and only if it has no strongly prime ideals. We investigate the question of when the left and right radical congruence relations of various radicals are equal. Some theorems analogous to theorems concerning the radicals of rings are also proved.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0369584-6
Keywords: Radicals of a semigroup, radical congruence, strongly prime ideal
Article copyright: © Copyright 1975 American Mathematical Society